This is a good question. I reckon it would be better to carry a tall slide around and a suit with a highish friction coeff as reversals of momentum involved in your plan seem like they would be completely fatal. This almost the sort of thing you could ask this guy: what-if.xkcd.com
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Nathan CooperDec 19 '12 at 11:01

6 Answers
6

Terminal velocity is a bit more than 50 m/s. The bottom of your ramp appears to have a radius less than 2m. That means you'll be exposed to more than 125g as you zip around the bottom. Nice knowing you.

Maybe you can estimate what the radius should be to make it work?
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BernhardDec 19 '12 at 9:41

accleration scales with 1/r, so multiply that by ten or so
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Mark EichenlaubDec 19 '12 at 10:52

4

Since you assume the scale of the drawing is relevant, may I point out that he is not falling very far and unlikely to have reached anything like terminal velocity? (Not to mention we don't know anything about drag on stick figures.)
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kojiroDec 19 '12 at 14:00

Also, consider that a very light ramp could also serve as a moderately effective parachute. It would at least affect the terminal velocity of the system.
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InvisibleBaconJan 11 '13 at 19:50

In the global, cartoon, sense, yes, this problem is equivalent to having a whole row of carefully designed, placed and arranged ramps so that you fall onto the first one, get "flung" out such that you then land on the next one and so on, until dissipation wastes away the energy. Obviously this can be done since it is the same principle as is used in say motorcycle jumps. The key feature is that you never experience accelerations large enough to kill you (it's not the fall that kills you, it's the sudden stop at the end).

It is all the details will cause problems.

First, with just a rope, you don't have any control over how/where the ramp will land, you may not hit the gentle slope-part and thus have a hard impact,

Note that the ramp itself will need to be strong enough to survive its own impact, as well as resisting the (ideally small) impact of your body. In addition, it will need to be large enough that the centripital (sic?) force applied to your body is small enough to not cause any damage (this is significantly larger than indicated in the drawings). This is a non-trivial design problem.

Another design aspect is the trade-off between having the ramp be light enough so that
your tethered connection to it doesn't hurt you, and having sufficient elasticity in the tether itself, the more slop in the tether. Note that having a large, low weight ramp will encounter more air-resistance, and thus you'd hit the ground before it.

You implied multiple bounces, this could be accomplished by arranging that you hit the ramp in the reverse direction for the second bounce. But again, there are control issues in ensuring that this would occur.

If you could somehow get the ramp to flip front to back as it flies though the air, it would be the right shape to catch you and fling you back up vertically. Repeat until non-lethal :)
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NathanielDec 19 '12 at 11:08

To put this in perspective: Apart from the speed lost due friction in the ramp (which, for the scale of it, won't make much of a difference) , when you exit the ramp you need to decelerate by applying the force to the ramp through the rope.

That is almost the same force that your body would suffer when crashing into the ground, only that concentrated in the parts of your body that hold the rope. If you hold the rope with your hands it will slip, if it is attached to your arm it will be probably torn off. Even with a more suited harness, your internal organs still will suffer the high deceleration that usually is the cause of death (remember, it is not the fall that kills, it is when you stop falling).

It is like throwing yourself from an airplane at 10,000 meters tied to a rope 9,995 meters long; when the rope stops descending you are in a big trouble.

As with bungee jumping, an elastic rope could offer a more suitable solution (as it allows applying the deceleration for a longer span of time, thereby needing less time), but at the speed you would be going then probably the rope will be either too inelastic, or too long for safely stop you before you hit the ground.

But remember, the only way to be sure is by trying! ]:)
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SJuan76Dec 19 '12 at 8:41

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The question states that the ramp is very light. The idea is that when you reach the end of the rope, the ramp is pulled up along with you without significantly slowing you down. It then lands on the ground ahead of you, ready to cushion your fall again. (The ramp, of course, is made of pure unobtainium.)
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Keith ThompsonDec 19 '12 at 8:52

@KeithThompson But the ramp cannot land ahead of you. The maximum velocity at which it can be projected is to your current velocity (because if it goes faster than you, the rope won't be tight and so it will not transmit any force). Once both you and the ramp go to the same velocity, since the main opposing force will be drag, the ramp will likely slow faster than you so it will never get ahead.
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SJuan76Dec 19 '12 at 9:41

A little elasticity in the rope might be enough to fling the ramp ahead of you. Not that the while idea is particularly realistic.
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Keith ThompsonDec 19 '12 at 9:48

This death roller coaster kills it's passengers by subjecting them to continuous 10g centrifugal acceleration, starving the brain for oxygen. The force is held constant regardless of friction, by reducing the radius of the circles.

I am posting this to illustrate that constant low-g acceleration can still kill you.

Due to terminal velocities (maybe we should concern about this velocity), a free-fall would end up atleast barely some $50 m/s$.

By light, I assume that you mean that the ramp is somewhat comparable (though it is massive) to your own weight. Then, it wouldn't definitely survive the crash. Such an impact wouldn't be survived by any known light materials (I think so). Would it be elastic, then you'd fall right away through it.

That oily friction part is somewhat encouraging. But, you couldn't carry such a massive body after you slide off. We've got two cases...

1) Assuming that your hand is robotic, you'll just rip your hand off which looks imaginary..!
2) The other one is worse. You'd leave away the rope (due to the same friction which discourages here)

Any way - You'll die: (But what about a new plan) You'd need a longer rope than you actually have now. Then, You could build an airbag-like ramp or something which automatically fills itself as it crashes the ground and then you could slide or roll or whatever...